Crofton's and Poincaré's formulas in the Lorentzian plane (Q793374)

The author gives the densities for points and lines (geodesics), the kinematic density and the density for pairs of points and pairs of lines in the sense of integral geometry, for the Lorentzian plane \((ds^ 2=dx^ 2-dy^ 2)\). Then, it is shown that Crofton's and Poincaré's classical formulas hold for piecewise pure curves (i.e. curves whose tangent vectors at every point are timelike or spacelike) with certain limitations for the angles between the curves and the intersection lines or between the intersection curves.